Related papers: On the paper "statistical approximation by positiv…
This paper is a corrigendum to the article 'On the ideal theorem for number fields`. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.
We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].
In this paper, using the concept of $A$-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a function $f$ by means…
A new Goodman-Sharma type modification of the Meyer-K\"{o}nig and Zeller operator for approximation of bounded continuous functions on [0,1) is presented. We estimate the approximation error of the proposed operator and prove direct and…
We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…
A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
This paper studies approximation properties of linear sampling operators in general Banach lattices $X$. We obtain matching direct and inverse approximation estimates, convergence criteria, equivalence results involving special…
In this short note, we improve the famous Reid Inequality related to linear operators.
This paper has been withdrawn by the author due to a crucial error.
This article describes counter example prepared in order to prove that linear formulation of TSP problem proposed in [arXiv:0803.4354] is incorrect (it applies also to QAP problem formulation in [arXiv:0802.4307]). Article refers not only…
Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414--1467, doi:10.1214/aop/1022677454] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35).…
In the present paper, we consider $(p,q)$-analogue of the Baskakov-Beta operators and using it, we estimate some direct results on approximation. Also, we represent the convergence of these operators graphically using MATLAB.
This paper has been withdrawn by the author(s), due a mistake of factor 1/2.
This paper has been withdrawn because Proposition 2.2 (c) is false. This invalids the main results of section 2 and 3. We thank A. Canonaco for pointing us the error.
This paper is withdrawn. We found a mistake in Lemma 4.1
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
In this article, we achieve some general statistical approximation results for $ \lambda $-Bernstein operators in addition to some other approximation properties. We prove a statistical Voronovskaja-type approximation theorem. We also…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
We find it absurd that Walliser [1] essentially used the same analysis and obtained identical results as reported in [3], yet arrived at different conclusions. Namely, based on an incomplete theory and using erroneous arguments, he not only…